Chapter 11.1, Problem 25IP

a.

To determine

To find: Value of $x$

Answer to Problem 25IP

Equation to find the value of $x$ is

  $2x^0+6x^0$

Value of $x$ is

  $x={22.5}^0$

Explanation of Solution

Given information:

Pair of angles

From the given figure

We can say that both angles forms a straight line

It means both angles are supplementary angles.

Therefore,

Sum of their measure is ${180}^0$

It means $2x^0+6x^0={180}^0$ is the equation to find the value of $x$

  $\begin{array}{l}2x^0+6x^0={180}^0\\ \Rightarrow 8x^0={180}^0\\ \Rightarrow x=\frac{{180}^0}{8}\\ \Rightarrow x={22.5}^0\end{array}$

Therefore,

Value of $x$ is ${22.5}^0$

b.

To determine

To find: Measure of two angles.

Answer to Problem 25IP

  ${135}^0$ and ${45}^0$ are two angles.

Explanation of Solution

Given information:

Pair of angles

From the given figure

We can say that both angles forms a straight line

It means both angles are supplementary angles.

Therefore,

Sum of their measure is ${180}^0$

It means $2x^0+6x^0={180}^0$ is the equation to find the value of $x$

  $\begin{array}{l}2x^0+6x^0={180}^0\\ \Rightarrow 8x^0={180}^0\\ \Rightarrow x=\frac{{180}^0}{8}\\ \Rightarrow x={22.5}^0\end{array}$

On substituting value of $x$ in both angles

We get

One of the angles is $=2x^0=2{\left(22.5\right)}^0={45}^0$

Other angle is $=6x^0=6{\left(22.5\right)}^0={135}^0$

Therefore,

  ${135}^0$ and ${45}^0$ are two angles.